Axford, 30, is 6-7 with a 4.45 ERA and 19 saves in 62 games this season. He led the National League with 46 saves in 2011.
Axford is expected to join the team on Friday night when they start a seven-game trip in Pittsburgh.
(Axford is) "a reliever that offers experience as both a setup man and closer. He's also a pitcher who brings familiarity with the NL Central, pennant-race baseball and the postseason," Cardinals general manager John Mozelia said about Axford.
Axford is making $5 million this season and will be eligible for arbitration in 2014.